布尔代数的I-V犹豫模糊子代数

I-V hesitant fuzzy sub-algebras of Boolean algebras

将布尔代数与犹豫模糊集相结合,首先,在布尔代数上定义了I-V犹豫模糊子代数,讨论I-V犹豫模糊子代数的性质以及若干等价刻画。其次,研究犹豫模糊集的水平集与布尔代数的子代数之间的关系,证明两个I-V犹豫模糊子代数的交仍是I-V犹豫模糊子代数,并且在布尔代数同态满射的前提下讨论布尔代数的I-V犹豫模糊子代数的像与原像的性质。最后,研究了布尔代数直积上的I-V犹豫模糊子代数。

Combining Boolean Algebra with hesitant fuzzy sets,firstly,the concept of I-V hesitant fuzzy sub-algebras of Boolean algebra is defined,and its properties and equivalent characterization are given.Secondly,the relationship between the level set of hesitant fuzzy sets and the sub-algebras of Boolean algebra is studied.It is proved that the intersection of two I-V hesitant fuzzy sub-algebras is still I-V hesitant fuzzy sub-algebras.Under the premise of homomorphic surjections of Boolean algebras,the properties of images and preimages of I-V hesitant fuzzy subalgebras of Boolean algebras are discussed.Finally,I-V hesitant fuzzy sub-algebras on the direct product of Boolean algebras are studied.